ARIMA

The ARIMA command estimates Univariate ARIMA models. There are 3 forms of the command: IDENTIFICATION, ESTIMATION, and FORECASTING. The specified options determine which form of the ARIMA command is in effect.


IDENTIFICATION PHASE

In general, the format is:

  ARIMA vars / options

where vars is a list of variables. The available options are:

Option Description
ALL Compute all orders up to and including NDIFFand NSDIFF.
IAC Compute inverse autocorrelations. (reference: Cleveland, Technometrics, 1972, pp.277-293)
GRAPHAC Prepare GNUPLOT plots for the PLOTAC, PLOTDATA, and GRAPHDATA PLOTPAC options.
GRAPHPAC
LOG Take logs of the data.
PLOTAC Plot autocorrelation function.
PLOTDATA Plot data.
PLOTPAC Plot partial autocorrelation function.
WIDE/NOWIDE Controls size of terminal screen output.
ACF= Saves the AutoCorrelation Function in the variable specified.
BEG= END= First and last observation to be used.
NDIFF= Order of differencing to transform the data.
NLAG= The number of lags for autocorrelations. The default is 24.
NLAGP= The number of lags for partial autocorrelations. The default is 12. (The value for NLAGP= must not exceed that for NLAG=).
NSDIFF= Order of Seasonal Differencing. If this is specified then NSPAN= must be set.
NSPAN= The number of periods for the seasonal cycle. For example, set NSPAN=4 for quarterly data and  NSPAN=12 for monthly data.
PACF= Saves the Partial AutoCorrelation Function in the variable specified.
TESTSTAT= Saves the Ljung-Box-Pierce statistics (computed at every lag) in the variable specified.

The available temporary variables are:
$N - the number of observations used in the identification phase.


ESTIMATION PHASE 

In general, the format is:

  ARIMA var / NAR= NMA= options

where var is a variable. The available options as used for the IDENTIFICATION phase are:
LOG, WIDE, BEG=, END=, NDIFF=, NSDIFF=, NSPAN=.

The available options as used for the OLS command are:
ANOVA, PCOR, PCOV, COV=, STDERR=, TRATIO=.

Other options are:

Option Description

DN 

Computes the estimated variance of the regression by dividing SIGMA**2 by N instead of (N-K).

GRAPHRES 

Prepare GNUPLOT plots for the PLOTRES option.

NOCONSTANT 

No intercept in model.

PITER 

Print every iteration.

PLOTRES 

Plot the residuals.

RESTRICT 

Use zero starting values as zero restrictions.

START 

Starting values for coefficients follow the ARIMA command.

ACF= 

Saves the AutoCorrelation Function of the estimated residuals in the variable specified.

COEF= 

Save Coefficients in variable specified.

ITER= 

Maximum number of iterations. The default is 50.

NAR= 

Order of the AR process. (REQUIRED)

NMA= 

Order of the MA process (REQUIRED).

NSAR= 

Order of the Seasonal AR process. If this is specified then NSPAN= must be set.

NSMA= 

Order of the Seasonal MA process. If this is specified then NSPAN= must be set.

PREDICT= 

Save Predicted values in variable specified.

RESID= 

Save Residuals in variable specified.

START= 

A vector of starting values.

TESTSTAT= 

Saves the Ljung-Box-Pierce statistics (computed at every lag -up to 60 lags) in the variable specified.

Following model estimation the available temporary variables as for the OLS command are:
$ERR, $K, $N, $R2, $SIG2, $SSE, $SSR, $SST.


FORECASTING PHASE

In general, the format is:

  ARIMA var / COEF= NAR= NMA= FBEG= FEND= options

where var is a variable. The available options as used for the IDENTIFICATION and ESTIMATION phase are:
LOG, NOCONSTANT, BEG=, END=, NAR=, NDIFF=, NMA=, NSAR=,
NSDIFF=, NSMA=, NSPAN=, PREDICT=, RESID=.

Other options are:

Option Description

GRAPHFORC 

Prepare GNUPLOT plots for the PLOTFORC option.

PLOTFORC 

Plot the forecast with error bounds.

COEF= 

Input coefficient variable. If this is not specified then coefficients must be entered on the line following the ARIMA command.

FBEG= 

The origin date of the forecast (required).

FEND= 

Last observation to forecast (required). (The maximum number of forecasts is 200.)

FCSE= 

Saves the forecast standard errors in the variable.

SIGMA= 

Used in calculating the forecast standard errors.

By default the data for the current sample period will be used to estimate SIGMA. A recommended approach is following estimation enter:

GEN1 S=SQRT($SIG2).

Then use the option SIGMA=S for the ARIMA forecasting.